Simplify (-2x^2)^-3(4x^8)

${(- 2 x^{2})}^{- 3} (4 x^{8})$

Rewrite using the commutative property of multiplication.

$4 {(- 2 x^{2})}^{- 3} x^{8}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$4 \frac{1}{{(- 2 x^{2})}^{3}} x^{8}$

Simplify the denominator.

Apply the product rule to $- 2 x^{2}$ .

$4 \frac{1}{{(- 2)}^{3} {(x^{2})}^{3}} x^{8}$

Raise $- 2$ to the power of $3$ .

$4 \frac{1}{- 8 {(x^{2})}^{3}} x^{8}$

Multiply the exponents in ${(x^{2})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$4 \frac{1}{- 8 x^{2 \cdot 3}} x^{8}$

Multiply $2$ by $3$ .

$4 \frac{1}{- 8 x^{6}} x^{8}$

Simplify terms.

Cancel the common factor of $4$ .

Factor $4$ out of $- 8 x^{6}$ .

$4 \frac{1}{4 (- 2 x^{6})} x^{8}$

Cancel the common factor.

$4 \frac{1}{4 (- 2 x^{6})} x^{8}$

Rewrite the expression.

$\frac{1}{- 2 x^{6}} x^{8}$

Cancel the common factor of $x^{6}$ .

Factor $x^{6}$ out of $- 2 x^{6}$ .

$\frac{1}{x^{6} \cdot - 2} x^{8}$

Factor $x^{6}$ out of $x^{8}$ .

$\frac{1}{x^{6} \cdot - 2} (x^{6} x^{2})$

Cancel the common factor.

$\frac{1}{x^{6} \cdot - 2} (x^{6} x^{2})$

Rewrite the expression.

$\frac{1}{- 2} x^{2}$

Combine $\frac{1}{- 2}$ and $x^{2}$ .

$\frac{x^{2}}{- 2}$

Move the negative in front of the fraction.

$- \frac{x^{2}}{2}$